Wow, I agree that a study of FarmVille sounds like a waste of money. But that doesn't make sense, why would the NSF fund a study like that? Well let's see...

The Fox News article's main source is a watchdog report released by Sen. Tom Coburn (R-Oklahoma) titled "National Science Foundation: Under the Microscope" (PDF). This report attempts to blow the whistle on excessive government spending through funding unnecessary science projects. On the topic of FarmVille, the Senator reports:

A $315,000 NSF study suggests playing FarmVille on Facebook helps adults develop and maintain relationships. The NSF-funded study, “The ‘S’ in social network games: Initiating, maintaining, and enhancing relationships,” has determined that many adults “are playing games such as Facebook’s FarmVille to help initiate, develop, and maintain relationships.” (source)

The report correctly cites the source of their information regarding the amount of NSF funding, which can be found in the award abstract (HCC 0916019). The Senator is correct that the NSF award is for almost $315,000 (actually $314,863), however the award does not provide funding for a solitary study. The award is a continuing two-year grant addressing the role of social network sites in facilitating collaborative processes.

So while the Senator's report is correct that the publication "The S in Social Network Games: Initiating, Maintaining, and Enhancing Relationships" (PDF) was funded by the National Science Foundation, this was not the sole publication resulting from the grant.

In fact, the same grant (HCC 0916019) funded studies that led to no less than 5 published articles on the topic of the role of social network sites in facilitating collaborative processes:

These are merely the studies that came up in a Google Scholar search, and acknowledge the NSF funding source in the text. Considering five publications resulting from the same two-year grant (and presumably two-year salary and research expenses), this research doesn't seem as wasteful as Senator Tom Coburn and Fox News would have you believe.

In fact, upon closer inspection, the study about FarmVille is the only publication funded by this grant that did not pay the subjects anything for their participation. The total amount paid to recruit participants for the other 4 studies totals $2,170. So of the studies funded by the grant, the study involving interviews of 18 unpaid subjects is surely the least wasteful in terms of recruiting participants.

Finally, the study that involved FarmVille was by no means a study ABOUT FarmVille. In fact, according to the published article, the interview protocol originally "focused on general questions about Facebook use as well as specific questions about relationship management" (source). After participants brought up games in their discussion of Facebook use, the researchers later added standard questions to more thoroughly probe the phenomena. In other words, the researchers did not set out to study FarmVille.